Two congressional staffers, speaking on condition of anonymity because the decision is pending, said Air Force officials began informing lawmakers Tuesday afternoon of the pending announcement.
Last month, a Government Accountability Office report said Boeing might have won the contract if the Air Force had not made mistakes in evaluating the competing bids. The GAO recommended the service hold a new competition.
Defense Secretary Robert Gates would not confirm when a decision would be made, but told reporters Tuesday: "I expect to announce the way forward very soon."
"I take the report from the Government Accountability Office very seriously, and particularly their identification of some deficiencies in the contract process," Gates said during a visit to Fort Lewis, Wash.
Gates is overseeing the decision on how the Air Force should respond.
The tanker deal -- one of the largest in Pentagon history -- is the first of three Air Force contracts worth up to $100 billion to replace an aging fleet of nearly 600 refueling tankers over the next 30 years.
Top acquisition officials from the Pentagon are set to testify on the award Thursday before the House Armed Services Air and Land Forces subcommittee.
Lawmakers from Washington state and Kansas, where Boeing employs thousands of workers, have put considerable pressure on the Air Force to reopen the bidding process and cancel the contract with Northrop Grumman Corp. and Airbus parent European Aeronautic Defence and Space Co.
"The Air Force could try anything from a quick fix to starting over," said Loren Thompson, a defense analyst at the Lexington Institute, an Arlington, Va.-based think tank.
But as a practical matter, Thompson said, any attempt that appears to ignore the GAO report would meet resistance in Congress, where lawmakers could move to block the Air Force from awarding the contract to Northrop Grumman.
Meanwhile, Sen. Patty Murray, D-Wash., introduced a Senate Resolution Tuesday calling on the Pentagon to rebid the flawed tanker contract.
"The GAO's decision was clear, and today we are reiterating that message so that the Pentagon knows there is no wiggle room," Murray said. "It's time to go back and hold a truly transparent competition that does our war fighters and taxpayers justice."
The resolution was co-sponsored by Sens. Pat Roberts, R-Kan., Kit Bond, R-Mo. and Claire McCaskill, D-Mo.
Sen. Richard Shelby, a Republican from Alabama, where the Northrop Grumman plane would be assembled, said he would support the bidders submitting revised proposals instead of a "full recompetition" to speed the process along.
"It is important to remember that the GAO's concerns were with procedural flaws in the Air Force's process, not with Northrop Grumman's product," Shelby said.